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WASHINGTON -- Meeting with Mexican officials today, Secretary of State Rex Tillerson declared "the wall does not define our relationship," while Homeland Security Secretary John Kelly said there’s room for "collaboration between Mexican authorities and U.S. authorities" in the "multifaceted" border security and drug interdiction solution.

The two met with Mexico's Foreign Secretary Luis Videgaray and Secretary of the Interior Miguel Angel Osorio for "very, very useful and fruitful conversations" on battling transnational criminal organizations, Tillerson said.

"While it was not a meeting where we reached new agreements or where specific strategies were developed, it was indeed a meeting where we were able to achieve fundamental agreements on the nature of the problem, on our diagnostics, and also an understanding that we need to tackle jointly all of the elements in the chain of this criminal business model. We need to overcome the blame game and the finger-pointing aspect," Videgaray said, adding of the drug trade, "We must understand that every demand creates supply and every supply creates demand."

"If the governments of Mexico and the United States discuss who’s to blame, who’s responsible, the only one who wins is organized crime that is bringing violence and death on both sides of the border," Videgaray added. "The time has come for us to dare think in a different way."

Osorio said that "both countries have agreed how urgent it is to work on a bi-national level in a more equitable way."

Tillerson acknowledged, "We know what we own, and we as Americans need to confront that we are the market" for the Mexican drug trade. "There is no other market for these activities. It is all coming here. But for us, Mexico wouldn’t have the trans-criminal organized crime problem and the violence that they’re suffering. And it’s – we really have to own up to that."

"There are so many areas of cooperation between our two countries, and we’re going to focus on those that we can make progress on now," the secretary of State added. "And there will be other talks to make progress on other areas of importance, including the renegotiation, restructuring of NAFTA."

Osorio noted that Mexico "is part of the problem," as drug production "has to be curtailed."

"So, basically, that’s the balance that we have to achieve, and it has to be based on these comprehensive talks, as Secretary Videgaray said. One of the issues is security," he said. "We have to work on that because we don’t want to give the idea that this violence is not being addressed on our side, and this is why we talked about the comprehensive issue on all the problems that both sides face and what are the alternatives that we could find to solve this issue together."